Related papers: Units and Augmentation Powers in Integral Group Ri…

In a previous paper [Homology cylinders: an enlargement of the mapping class group, Algebr. Geom. Topol. 1 (2001) 243--270, arXiv:math.GT/0010247], a group H_g of homology cylinders over the oriented surface of genus g is defined. A…

Given a collection $\{ G_i\}_{i=1}^d$ of finite groups and a ring $R$, we have previously introduced and studied certain foundational properties of the join ring $\mathcal{J}_{G_1, G_2, \ldots, G_d}(R)$. This ring bridges two extreme…

Zassenhaus Conjecture for torsion units states that every augmentation one torsion unit of the integral group ring of a finite group G is conjugate to an element of G in the units of rational group algebra QG. This conjecture has been…

We establish upper and lower bounds on the dimension of the space spanned by the symmetric powers of the natural character of generalised symmetric groups. We adapt the methods of Savitt and Stanley from their paper `A note on the symmetric…

In this paper we study distortion of various well-known embeddings of finitely generated torsion-free nilpotent groups $G$ into unitriangular groups $UT_n(\mathbb{Z})$. We also provide a polynomial time algorithm for finding distortion of a…

For a general linear supergroup $G=GL(m|n)$, we consider a natural isomorphism $\phi: G \to U^-\times G_{ev} \times U^+$, where $G_{ev}$ is the even subsupergroup of $G$, and $U^-$, $U^+$ are appropriate odd unipotent subsupergroups of $G$.…

We study the ring of arithmetical functions with unitary convolution, giving an isomorphism to a generalized power series ring on infinitely many variables, similar to the isomorphism of Cashwell-Everett between the ring of arithmetical…

For a group $G$ and a subgroup $H$ of $G$ this article discusses the normalizer of $H$ in the units of a group ring $RG$. We prove that $H$ is only normalized by the `obvious' units, namely products of elements of $G$ normalizing $H$ and…

Unitary transformations and density matrices are central objects in quantum physics and various tasks require to introduce them in a parameterized form. In the present article we present a parameterization of the unitary group…

Tilting modules, generalising the notion of progenerator, furnish equivalences between pieces of module categories. This paper is dedicated to study how much these pieces say about the whole category. We will survey the existing results in…

Let G be a finite group with a generating set A. By the (symmetric) diameter of G with respect to A we mean the maximum over g in G of the length of the shortest word in (A union A inverse)A expressing g.By the (symmetric) diameter of G we…

We analyze the universal size characteristics of flexible ring polymers in solutions in presence of structural obstacles (impurities) in d dimensions. One encounters such situations when considering polymers in gels, colloidal solutions,…

This is mainly a small exposition on extensions of valuation rings as a filtered union of smooth algebras.

This article first answers to questions about connectedness of a new family of graphs on unicellular maps. Answering these questions goes through a description of the mapping class group as surgeries on unicellular maps. We also show how…

The asymptotic behavior of graded Betti numbers of powers of homogeneous ideals in a polynomial ring over a field has recently been reviewed. We extend quasi polynomial behavior of graded Betti numbers of powers of homogenous ideals to…

The group ring of the automorphism group of a p-group is studied using the automorphism groups of subgroups and quotient groups of P.

We make a systematic study of filtrations of a free group F defined as products of powers of the lower central series of F. Under some assumptions on the exponents, we characterize these filtrations in terms of the group algebra, the Magnus…

We show how to use the combinatorial notion of jump sets to parametrize the possible structures of the group of principal units of local fields, viewed as filtered modules. We establish a natural bijection between the set of jump sets and…

The relationship between mappings of sets and renormalization group transformations is established, and renormalization group invariants of such mappings are found. These results are valid both for continuous and discrete mappings and for…

This paper introduces and studies the higher-order group inverse in a ring. We extend known properties of the higher-order group inverse from complex matrices to elements of a ring and, in the process, derive new results. We further…